TY - JOUR

T1 - Newton Polygon Stratification of the Torelli Locus in Unitary Shimura Varieties

AU - Li, Wanlin

AU - Mantovan, Elena

AU - Pries, Rachel

AU - Tang, Yunqing

N1 - Publisher Copyright:
© 2020 The Author(s) 2020. Published by Oxford University Press. All rights reserved.

PY - 2022/5/1

Y1 - 2022/5/1

N2 - We study the intersection of the Torelli locus with the Newton polygon stratification of the modulo p reduction of certain Shimura varieties. We develop a clutching method to show that the intersection of the open Torelli locus with some Newton polygon strata is non-empty. This allows us to give a positive answer, under some compatibility conditions, to a question of Oort about smooth curves in characteristic p whose Newton polygons are an amalgamate sum. As an application, we produce infinitely many new examples of Newton polygons that occur for smooth curves that are cyclic covers of the projective line. Most of these arise in inductive systems that demonstrate unlikely intersections of the open Torelli locus with the Newton polygon stratification in Siegel modular varieties. In addition, for the 20 special Shimura varieties found in Moonen's work, we prove that all Newton polygon strata intersect the open Torelli locus (if p>>0 in the supersingular cases).

AB - We study the intersection of the Torelli locus with the Newton polygon stratification of the modulo p reduction of certain Shimura varieties. We develop a clutching method to show that the intersection of the open Torelli locus with some Newton polygon strata is non-empty. This allows us to give a positive answer, under some compatibility conditions, to a question of Oort about smooth curves in characteristic p whose Newton polygons are an amalgamate sum. As an application, we produce infinitely many new examples of Newton polygons that occur for smooth curves that are cyclic covers of the projective line. Most of these arise in inductive systems that demonstrate unlikely intersections of the open Torelli locus with the Newton polygon stratification in Siegel modular varieties. In addition, for the 20 special Shimura varieties found in Moonen's work, we prove that all Newton polygon strata intersect the open Torelli locus (if p>>0 in the supersingular cases).

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U2 - 10.1093/imrn/rnaa306

DO - 10.1093/imrn/rnaa306

M3 - Article

AN - SCOPUS:85113437099

VL - 2022

SP - 6464

EP - 6511

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 9

ER -